<p>The development of active and inexpensive catalysts is vital for progress in technologies related to efficient energy generation, storage, and utilization. Transition metal oxides (TMOs) make up a significant fraction of current state-of-the-art catalysts for these technologies. Density functional theory (DFT), the workhorse for computational chemistry and catalysis, can calculate the activity of catalysts, provide synthesis targets, and accelerate the discovery of active and cheap TMO catalysts. This dissertation develops DFT methods for accurately calculating and understanding the catalytic activity of TMOs. Known electron self-interaction errors in TMO bulk oxidation energies implies reactions energies on TMO surfaces should contain similar errors. The linear response U, proposed to correct self-interaction error, was evaluated as a method for obtaining more accurate TMO reaction energies. Application of the linear response U gave unprecedented improvement in TMO oxidation energies, mixed improvement in TMO formation energies, and improved trends in TMO surface reactivity. These results motivate the continued development of linear response U for bulk and surface calculations. The calculated electronic structure of a catalyst can be used to relate its structure and composition to its activity. Physical and chemical complexities of TMOs hinder development of useful and elucidative electronic structure models. Using the understanding of adsorption on metals as a foundation, a number of correlations between the calculated electronic structure and adsorption energy were found on TMO surfaces. These correlations led to structure-function relationships of binary, ternary, and polymorph TMOs. Methods and results used provides research directions on the continued search for new transition metal compound catalysts.</p>